How to create Wind effect on circle logo
So as I said you can cut a grid with the Knife Project tool. Then to make it work properly, first create the pin group:

Choose Cloth &gt; Cotton for example. Create a Force Field &gt; Wind and a Force Field &gt; Turbulence. Make the Wind rotate and vary its Strength value through time. Maybe also create a simple edge and give the circle object a Copy Scale constraint with the edge as Target, and change the height of the edge a bit so that the circle vary its height a bit as well, it will create more folds: